Question

Find the LCM of the following numbers by the common division method.

$90,126,135,255$

Answer 1

In common division method we divide the numbers whose LCM we need to by common prime divisors, and leave the division when we are left with co-prime numbers.

Step 1 : Divide the numbers by common prime divisors.

$2$	$90,126,135,255$
$3$	$45,63,135,255$
$3$	$15,21,45,85$
$5$	$5,7,15,85$
	$1,7,3,17$

We will stop as we have two co-prime numbers.

Step 2 : Multiply the remaining co-prime numbers and the common prime divisors to get the LCM

LCM is $2\times 3\times 3\times 5\times 7\times 3\times 17=32130$